A particular flight from Chicago to Orlando has 224 seats Si

A particular flight from Chicago to Orlando has 224 seats. Since it is well documented that not all passengers show up for their seat reservation, the airline overbooks the flight by accepting more than 224 reservations. If the flight is not overbooked, the airline loses money due to open seats, but if too many seats are sold and some passengers are denied seats, then the airline loses money for the compensation it must give to those passengers.

Assume that there is a .0895 probability that a passenger with a reservation on this flight will not show up. Also assume that the airline accepts 245 reservations for the 224 seats available.

What is the probablility that out of 245 booked reservations, exactly 224 people show up for the flight? What is the probability no more than 224 people show up? How are these two probabilities different?

Solution

Probability that a passenger with a reservation will show up = 1 - 0.0895 = 0.9105

Total no.of passengers who will show up = 245 * 0.9105 = 223.07

Since , 223.07<224

The probability that more than 224 people with reservations actually show up for the flight = 0 Answer

The probability of overbooking small so that it does not appear very often.